Arithmetic Course/Non Linear Function/Exponential function/Exponential growth

Exponential Growth

Exponential Growth function is a function that has the value growth exponentially

$N(t)=N_0{e}^{\lambda t}.$

Which can be proven as the root of a Differential Equation of the form

$\frac{dN}{dt}=\lambda N.$

Proof

For a Differential Equation of the form

$\frac{dN}{dt}=\lambda N.$

$\int \frac{dN}{N}=\lambda \int dt$

$lnN=\lambda t+c$

$N=e^{(}\lambda t+c)$

$N(t)=N_0{e}^{\lambda t}.$